У пра 1. Задайте перечислением элементов множество, заданное ха-
рактеристическим свойством:
а) А = | ? + 2x – 8 = 0
I
б) B = {x |x EN, 2<x<s}} :
в) C = {x |х єN, х4 -5х2 + 4 = 0};
г) D= {x | xel, -5 < x +1< 20};
д) E = {(x, y) | (x-1)2 + (у + 2)2 = 0}:
c) F = {x | xez, i < 5}:
ж) P= {x | хєN, – 4 < x < 6};
3) Q= {n |neN, n< 20, n – простое):
и) S
- не г.
1
n? - 2n +5
E Z,
— целое
(n — 1)?
к) Т = {x | xeN, – х*+x+62 0}.
1) 2cosx-1 < 0
cosx < 1/2
arccos(1/2) + 2πn < x < 2π - arccos(1/2) + 2πn, n ∈ Z
π/3 + 2πn < x < 2π - π/3 + 2πn, n ∈ Z
π/3 + 2πn < x < 5π/3 + 2πn, n ∈ Z
2) sin2x - √2/2 < 0
sin2x < √2/2
- π - arcsin(√2/2) + 2πk < 2x < arcsin(√2/2) + 2πk, k ∈ Z
- π - π/4 + 2πk < 2x < π/4 + 2πk, k ∈ Z
- 5π/4 + 2πk < 2x < π/4 + 2πk, k ∈ Z
- 5π/8 + πk < x < π/8 + πk, k ∈ Z
3) tgx<1
- π/2 + πn < x < arctg(1) + πn, n ∈ Z
- π/2 + πn < x < π/4 + πn, n ∈ Z
b1q + b1q^2 = 14 разделим первое уравнение на 2-е
(1 + q^3)/(q +q^2) = -7/2
(1+q)(1 -q +q^2)/q(1 +q) = -7/2
(1 -q +q^2) /q = -7/2
2(1 - q +q^2) = -7q
2 -2q +2q^2 +7q = 0
2q^2 +5q +2 = 0
D = b^2 -4ac = 25 -16 = 9
q1= -1/2, a) b1 + b1q^3 = -49 б) q2 =-2 b1 + b1q^3 = -49
b1 +b1*(-1/8) = -49 b1 + b1*(-8) = -49
7/8 b1 = -49 -7b1 = -49
b1 = -49: 7/8= -49*8/7= =56 b1 = 7